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Each of the following statements is an attempt to show that a given series is convergent or divergent using the Comparison Test (NOT the Limit Comparison Test.) For each statement, enter C (for "correct") if the argument is valid, or enter I (for "incorrect") if any part of the argument is flawed. (Note: if the conclusion is true but the argument that led to it was wrong, you must enter 1.) 1. For all ʼn > 1, the Comparison Test, the series > n 2. For all n>2, 72³—2 by the Comparison Test, the series > 3. For all n > 2, In(n) n n 2-n³ the Comparison Test, the series > 4. For all n > 1, < and the series Σ 1 7²1 1 nln(n) In(n) n² In(n) 7² N 2-73 Converges. A 2 7², n n n³-2 converges. n the Comparison Test, the series (n) diverges. 5. For all n > 2, 1, and the series > diverges, so by n' In(n) n 1 1 7², and the series 21/1/2 In(n) the Comparison Test, the series > n² 1 6. For all n > 1, 71.5, converges, so by diverges. and the series 2 diverges, so by converges. and the series Σ converges. converges, so and the series converges, so by In(n) by the Comparison Test, the series > n² n 715 Converges, so

Each of the following statements is an attempt to show that a given series is convergent or divergent using the Comparison Test (NOT the Limit Comparison Test.) For each statement, enter C (for "correct") if the argument is valid, or enter I (for "incorrect") if any part of the argument is flawed. (Note: if the conclusion is true but the argument that led to it was wrong, you must enter 1.) 1. For all ʼn > 1, the Comparison Test, the series > n 2. For all n>2, 72³—2 by the Comparison Test, the series > 3. For all n > 2, In(n) n n 2-n³ the Comparison Test, the series > 4. For all n > 1, < and the series Σ 1 7²1 1 nln(n) In(n) n² In(n) 7² N 2-73 Converges. A 2 7², n n n³-2 converges. n the Comparison Test, the series (n) diverges. 5. For all n > 2, 1, and the series > diverges, so by n' In(n) n 1 1 7², and the series 21/1/2 In(n) the Comparison Test, the series > n² 1 6. For all n > 1, 71.5, converges, so by diverges. and the series 2 diverges, so by converges. and the series Σ converges. converges, so and the series converges, so by In(n) by the Comparison Test, the series > n² n 715 Converges, so

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Each of the following statements is an attempt to show that a given series is convergent or divergent using the Comparison Test (NOT the Limit Comparison Test.) For each statement, enter C (for "correct") if the argument is valid, or enter I (for "incorrect") if any part of the argument is flawed. (Note: if the conclusion is true but the argument that led to it was wrong, you must enter 1.) 1. For all ʼn > 1, the Comparison Test, the series > n 2. For all n > 2, 72²³–2 n 2-n³ < and the series Σ 1 7²1 the Comparison Test, the series > 4. For all n > 1, 1 nln(n) the Comparison Test, the series 5. For all n > 2, In(n) n by the Comparison Test, the series > n³-2 converges. In(n) 3. For all n > 2, n the Comparison Test, the series > 6. For all n > 1, In(n) 7² N 2-73 Converges. A 2 7², n n 1 and the series diverges, so by n " In(n) n 1 n², 1 In(n) n² and the series 21/1/2 1 n1.5, converges, so by (n) diverges. and the series converges, so by diverges. and the series 2 diverges, so by converges. and the series Σ converges. converges, so In(n) by the Comparison Test, the series > .7² n 715 Converges, so
Transcribed Image Text:Each of the following statements is an attempt to show that a given series is convergent or divergent using the Comparison Test (NOT the Limit Comparison Test.) For each statement, enter C (for "correct") if the argument is valid, or enter I (for "incorrect") if any part of the argument is flawed. (Note: if the conclusion is true but the argument that led to it was wrong, you must enter 1.) 1. For all ʼn > 1, the Comparison Test, the series > n 2. For all n > 2, 72²³–2 n 2-n³ < and the series Σ 1 7²1 the Comparison Test, the series > 4. For all n > 1, 1 nln(n) the Comparison Test, the series 5. For all n > 2, In(n) n by the Comparison Test, the series > n³-2 converges. In(n) 3. For all n > 2, n the Comparison Test, the series > 6. For all n > 1, In(n) 7² N 2-73 Converges. A 2 7², n n 1 and the series diverges, so by n " In(n) n 1 n², 1 In(n) n² and the series 21/1/2 1 n1.5, converges, so by (n) diverges. and the series converges, so by diverges. and the series 2 diverges, so by converges. and the series Σ converges. converges, so In(n) by the Comparison Test, the series > .7² n 715 Converges, so
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